Natural convection in right-angle porous trapezoidal enclosure partially cooled from inclined wall

A numerical study is conducted to investigate the steady free convection flow in a two-dimensional right-angle trapezoidal enclosure filled with a fluid-saturated porous medium. The left vertical wall of the cavity is heated; the inclined wall is partially cooled; and the remaining walls are insulated (adiabatic). Three different cases are considered. While in Case I the cooler wall is located adjacent to the top wall, in Case II it is located in the middle inclined wall. In Case III, it is located adjacent to the bottom wall. Flow and heat transfer characteristics are studied for a range of parameters: the Rayleigh number, Ra, 100 ≤ Ra ≤ 1000; and the aspect ration, AR = 0.25, 0.50 and 0.75. Numerical results indicate that there exist significant changes in the flow and temperature fields as compared with those of a differentially heated square porous cavity. These results lead, in particular, to the prediction of a position of minimum heat transfer across the cavity, which is of interest in the thermal insulation of buildings and other areas of technology.     

Numerical investigation of pulsating flow around a discrete heater in a channel

In this study, the forced convection heat transfer around a discrete heater located in a channel subjected to laminar pulsating air flow is numerically investigated. Simulations are conducted for six different frequencies and three different amplitudes, while the Reynolds number (Re = 125) and Prandtl number (Pr = 0.71) remain constant for all cases. The impact of the important governing parameters such as the Womersley number (Wo) and the amplitude of flow pulsation (A_o) on heat transfer rate from discrete heaters is examined in detail. The instant velocity and temperature profiles are obtained to determine of the role of dimensionless parameters for pulsating flow. The numerical results show that thermal transport from the heater is greatly affected by the frequency and amplitude of the flow pulsation. The results given are dimensionless parameters.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

Mixed convection heat transfer in a ventilated cavity with hot obstacle: Effect of nanofluid and outlet port location

In the present study, the lattice Boltzmann method is implemented to investigate the effect of suspension of nanoparticles on mixed convection in a square cavity with inlet and outlet ports and hot obstacle in the center of the cavity. The effect of outlet port location is examined on heat transfer rate then the effect of nanoparticles is inspected for volume fraction of nanoparticles in the range of 0 to 0.03 at the different position of outlet port. The study was carried out for different Richardson numbers ranging from 0.1 to 10. Grashof number is assumed to be constant (10⁴) so that the Richardson number changes with Reynolds number. The isothermal boundary condition is assumed for obstacle walls and the cavity walls are adiabatic. The result is presented by isotherms, streamlines, and local and average Nusselt numbers. The maximum heat transfer rate occurs when the outlet port is located at P2 for Ri = 0.1 and P1 for Ri = 1, Ri = 10, respectively. Results show that by adding the nanoparticles to base fluid and increasing the volume concentration of nanoparticles the heat transfer rate is enhanced at different Richardson numbers and outlet port positions. But this phenomenon is not observed at Ri = 10 when the outlet port is located at P1.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Natural convection of water-based nanofluids in an inclined enclosure with a heat source

This study investigates natural convection heat transfer of water-based nanofluids in an inclined square enclosure where the left vertical side is heated with a constant heat flux, the right side is cooled, and the other sides are kept adiabatic. The governing equations are solved using polynomial differential quadrature (PDQ) method. Calculations were performed for inclination angles from 0° to 90°, solid volume fractions ranging from 0% to 20%, constant heat flux heaters of lengths 0.25, 0.50 and 1.0, and a Rayleigh number varying from 10⁴ to 10⁶. The ratio of the nanolayer thickness to the original particle radius is kept at a constant value of 0.1. The heat source is placed at the center of the left wall. Five types of nanoparticles are taken into consideration: Cu, Ag, CuO, Al₂O₃, and TiO₂. The results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. The results also show that the length of the heater is also an important parameter affecting the flow and temperature fields. The average heat transfer decreases with an increase in the length of the heater. As the heater length is increased, the average heat transfer rate starts to decrease for a smaller inclination angle (it starts to decrease with inclination at 90° for ? = 0.25, 60° for ? = 0.50, 45° for ? = 1.0, respectively).     

Visualization of heat flow in a vertical channel with fully developed mixed convection

A study on visualization of heat flow in three channels with laminar fully developed mixed convection heat transfer is performed. The first channel is filled with completely pure fluid; the second one is completely filled with fluid saturated porous medium. A porous layer exists in the half of the third channel while another half is filled with pure fluid. The velocity, temperature and heat transport fields are obtained both by using analytical and numerical methods. Analytical expression for heat transport field is obtained and presented. The heatline patterns are plotted for different values of Gr/Re, thermal conductivity ratio, Peclet and Darcy numbers. It is found that the path of heat flow in the channel strongly depends on Peclet number. For low Peclet numbers (i.e., Pe = 0.01), the path of heat flow is independent of Gr/Re and Darcy numbers. However, for high Peclet numbers (i.e., Pe = 5), the ratio of Gr/Re, Darcy number and thermal conductivity ratio influence heatline patterns, considerably. For the channels with high Peclet number (i.e., Pe = 5), a downward heat flow is observed when a reverse flow exits.     

Experimental and numerical study on heat transfer enhancement in a channel with Z-shaped baffles

The influence of baffle turbulators on heat transfer augmentation in a rectangular channel has been investigated experimentally and numerically. In the experiment, the baffles are placed in a zigzag shape (Z-shaped baffle) aligned in series on the isothermal-fluxed top wall, similar to the absorber plate of a solar air heater channel. The aim at using the Z-baffles is to create co-rotating vortex flows having a significant influence on the flow turbulence intensity leading to higher heat transfer enhancement in the tested channel. Effects of the Z-baffle height and pitch spacing length are examined to find the optimum thermal performance for the Reynolds number from 4400 to 20,400. The Z-baffles inclined to 45° relative to the main flow direction are characterized at three baffle- to channel-height ratios (e/H = 0.1, 0.2 and 0.3) and baffle pitch ratios (P/H = 1.5, 2 and 3). The experimental results show a significant effect of the presence of the Z-baffle on the heat transfer rate and friction loss over the smooth channel with no baffle. The Nusselt number, friction factor and thermal performance enhancement factor for the in-phase 45° Z-baffles are found to be considerably higher than those for the out-phase 45° Z-baffle at a similar operating condition. The in-phase 45° Z-baffle with larger e/H provides higher heat transfer and friction loss than the one with smaller e/H while the shorter pitch length yields the higher Nu, f and TEF than the larger one. The numerical work is also conducted to investigate the flow friction and heat transfer behaviors in the channel mounted with the 45° Z-baffles, and the numerical results are found in good agreement with experimental data.     

Numerical modeling of the electrohydrodynamic effect to natural convection in vertical channels

The electrohydrodynamic effect to natural convection inside the vertical channels is numerically investigated by computational fluid dynamics technique. The range of parameters considered are 10⁴ = Ra = 10⁷, 7.5 = V₀ = 17.5 kV, and 2 = aspect ratio = 10. Flow and temperature distributions are affected with supplied voltage at the wire electrodes, and the heat transfer enhancement is significantly influenced at low Rayleigh number. The augmented volume flow rate of fluid is indicated in relation with the number of electrodes. Moreover, heat transfer enhancement also depended on the electrode arrangement while the number of electrodes is initially fixed. The relation between channel aspect ratio and number of electrodes that performs the maximum heat transfer is expressed incorporating with the optimum concerning parameters.     

Periodic laminar flow and heat transfer in a channel with 45° staggered V-baffles

A numerical investigation has been carried out to examine periodic laminar flow and heat transfer characteristics in a three-dimensional isothermal wall channel of aspect ratio, AR = 2 with 45° staggered V-baffles. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 1200. To generate two pair of main streamwise vortex flows through the tested section, V-baffles with an attack angle of 45° are mounted in tandem and staggered arrangement on the lower and upper walls of the channel. Effects of different baffle heights on heat transfer and pressure drop in the channel are studied and the results of the V-baffle pointing upstream are also compared with those of the V-baffle pointing downstream. It is apparent that in each of the main vortex flows, a pair of streamwise twisted vortex (P-vortex) flows can induce impinging flows on a sidewall and a wall of the interbaffle cavity leading to drastic increase in heat transfer rate over the channel. In addition, the rise in the V-baffle height results in the increase in the Nusselt number and friction factor values. The computational results reveal that the optimum thermal enhancement factor is around 2.6 at baffle height of 0.15 times of the channel height for the V-baffle pointing upstream while is about 2.75 at baffle height of 0.2 times for the V-baffle pointing downstream.     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.     

Conjugate natural convection in air filled tube inserted a square cavity

Numerical analyses of fluid flow and heat transfer due to buoyancy forces in a tube inserted square cavity filled with fluid were carried out by using control volume method in this study. The cavity was heated from the left wall and cooled from the right isothermally and horizontal walls were adiabatic. A circular tube filled with air was inserted into the square cavity. The case that the inside and outside of the tube were filled with the same fluid (air) was examined. Varied solid materials were chosen as the tube wall. Results were obtained for different Rayleigh numbers (Ra = 10⁴, 10⁵ and 10⁶), thermal conductivity ratio of the fluid to the tube wall (k = 0.1, 1 and 10) and different location centers of the tube (c (0.25 ≤ x ≤ 0.75, 0.25 ≤ y ≤ 0.75)). Comparison with benchmark solutions of the natural convection in a cavity was performed and numerical results gave an acceptable agreement. It was found that varied location of the tube center can lead to different flow fields and heat transfer intensities which are also affected by the value of Rayleigh number.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Second law analysis in a three dimensional lid-driven cavity

Three dimensional analyses of laminar mixed convection and entropy generation in a cubic lid-driven cavity have been performed numerically. Left side of cavity moves in + y (Case I) or −y (Case II) direction. The cavity is heated from left side and cooled from right while other surfaces are adiabatic. Richardson number is the main parameter which changes from 0.01 to 100. Prandtl number is fixed at Pr = 0.71. Results are presented by isotherms, local and mean Nusselt number, entropy generation due to heat transfer and fluid friction, velocity vectors and Bejan number. Total entropy generation contours are also presented. It is found that direction of lid is an effective parameter on both entropy generation and heat and fluid flow for low values of Richardson number but it becomes insignificant at high Richardson number.     

Numerical investigation of laminar heat transfer in a square channel with 45° inclined baffles

A numerical investigation of laminar periodic flow and heat transfer in a three-dimensional isothermal-wall square channel fitted with 45° inclined baffles on one channel wall is carried out in the present work. The finite volume method is introduced and the SIMPLE algorithm has been implemented for all computations. The fluid flow and heat transfer characteristics are presented for Reynolds numbers ranging from 100 to 1200. The 45° baffle mounted only on the lower channel wall has a height of b and an axial pitch length (L) equal to channel height (H). Effects of flow blockage ratios, BR = b/H = 0.1–0.5, on heat transfer and pressure loss in the square channel are examined and also compared with the typical case of the transverse baffle (or 90° baffle). It is found that apart from the rise of Reynolds number, the increase in the blockage ratio with the attack angle (α) of 45° results in considerable increases in the Nusselt number and friction factor values. The use of the 45° baffle can help to generate a streamwise main vortex flow throughout the channel leading to fast and chaotic mixing of flow between the core and the wall regions. In addition, the computational results reveal that the significant increase in heat transfer rate is due to impingement jets induced by a longitudinal vortex pair (P-vortex) of flow, appearing on the upper, lower and baffle trailing end side walls. The appearance of vortex-induced impingement flows created by the baffles leads to the maximum thermal enhancement factor of about 2.2 at BR = 0.4 and Re = 1200. The enhancement factor of the 45° baffle investigated is found to be higher than that of the 90° baffle for all Reynolds numbers and baffle heights.     

Study on thermal and fluid flow characteristics in turbulent channel flows with multiple twisted tape vortex generators

This research has been performed to study the influences of multiple twisted tape vortex generators (MT-VG) on the heat transfer and fluid friction characteristics in a rectangular channel. The experiments conducted using the twisted tapes with three different twist ratios (y/w = 2.5, 3.0 and 3.5) for generating different swirl and turbulent intensities in the channel. The twisted tapes are assembled to obtained the MT-VG with three different free-spacing ratios, s/w = 1.66 (5 tapes), s/w = 1.25 (7 tapes) and s/w = 1.0 (9 tapes). The results for the Reynolds number ranged from 2700 to 9000 at constant Prandtl number, Pr = 0.7, using air as the test fluid, are examined. In the studied range, the presence of channel with MT-VG leads to increase in heat transfer rate over the use of smooth channel around 10.3 to 169.5%. The channel with the smaller twist ratio (y/w) and free-spacing ratio (s/w) provides higher heat transfer rate and pressure loss than those with the larger of twist ratio and free-spacing ratio under similar operation conditions. In addition, correlations of Nusselt number (Nu) and friction factor (f) have been developed and the thermal enhancement index at constant pumping power is also determined.     

Thermal behavior in solar air heater channel fitted with combined rib and delta-winglet

Effects of combined ribs and delta-winglet type vortex generators (DWs) on forced convection heat transfer and friction loss behaviors for turbulent airflow through a solar air heater channel are experimentally investigated in the present work. Measurements are carried out in the rectangular channel of aspect ratio, AR = 10 and height, H = 30 mm. The flow rate is presented in the form of Reynolds numbers based on the inlet hydraulic diameter of the channel ranging from 5000 to 22,000. The cross-section shape of the rib placed on the absorber plate to create a reverse-flow is an isosceles triangle with a single rib height, e/H = 0.2 and rib pitch, P_l/H = 1.33. Ten pairs of the DW with its height, b/H = 0.4; transverse pitch, P_t/H = 1 and three attack angles (α) of 60°, 45° and 30° are introduced and mounted on the lower plate entrance of the tested channel to generate longitudinal vortex flows. The experimental results show that the Nusselt number and friction factor values for combined rib and DW are found to be much higher than those for the rib/DW alone. The larger attack angle of the DW leads to higher heat transfer and friction loss than the lower one. In common with the rib, the DW pointing upstream (PU-DW) is found to give higher heat transfer rate and friction loss than the DW pointing downstream (PD-DW) at a similar operating condition. In comparison, the largest attack angle (α = 60°) of the PU-DW yields the highest increase in both the Nusselt number and friction factor while the lowest attack angle of the PD-DW provides the best thermal performance.     

Control of mixed convection in lid-driven enclosures using conductive triangular fins

Control of mixed convection (combined forced and natural convection) in a lid-driven square cavity is performed using a short triangular conductive fin. A numerical technique is used to simulate the flow and temperature fields. The vertical walls of the cavity are differentially heated. Both the top lid and the bottom wall are adiabatic. The fin is located on one of the motionless walls of the cavity. Three different cases have been studied based on the location of the fin. In this context, Cases I, II and III refer to the fin on the left, bottom and right walls, respectively. Results are presented for +x and −x directions of the top lid in horizontal axis and different Richardson numbers as Ri = 0.1, 1.0 and 10.0. It is observed that the triangular fin is a good control parameter for heat transfer, temperature distribution and flow field.     

Analysis of fluid flow and heat transfer in a rib grit roughened surface solar air heater using CFD

This paper presents the study of fluid flow and heat transfer in a solar air heater by using Computational Fluid Dynamics (CFD) which reduces time and cost. Lower side of collector plate is made rough with metal ribs of circular, square and triangular cross-section, having 60° inclinations to the air flow. The grit rib elements are fixed on the surface in staggered manner to form defined grid. The system and operating parameters studied are: e/D_h = 0.044, p/e = 17.5 and l/s = 1.72, for the Reynolds number range 3600-17,000. To validate CFD results, experimental investigations were carried out in the laboratory. It is found that experimental and CFD analysis results give the good agreement. The optimization of rib geometry and its angle of attack is also done. The square cross-section ribs with 58° angle of attack give maximum heat transfer. The percentage enhancement in the heat transfer for square plate over smooth surface is 30%.     

Influence of exit opening location on mixed convection in a channel with volumetric heat sources

Mixed convection heat transfer in a channel with volumetric heat source and different opening ratio at the exit has been analyzed numerically. Steady, laminar, two-dimensional model based on the finite-volume method is used for solving the mass, momentum and energy transfer governing equations. The flow is injected to the duct with a uniform velocity distribution. The problem is studied in three aspect ratios (A = 1, 3 and 5) and three opening cases as single opening near the ceiling, single opening near the bottom and double openings. The study is also tested for different Richardson numbers between 0.01 and 10. Streamlines, isotherms, Nusselt numbers and temperature profiles were obtained for indicated cases. It is found that both the Richardson number and the locations of exit openings have strong effects on flow and temperature distribution in the presence of volumetric heat sources. The highest heat transfer was formed when the outlet port is located onto top of vertical wall.